Journal of Holography Applications in Physics
Thermodynamics of Noncommutative Geometry Inspired Regular Black Holes Coupled with Nonlinear Electrodynamics
Document Type : Regular article
Authors
1 Department of Physics, Dyal singh College, University of Delhi, New Delhi 110003, India
2 Department of Physics, Rajdhani College, University of Delhi, New Delhi 110015, India
3 Department of Civil Engineering, Faculty of Engineering, Marwadi University, Rajkot, Gujrat 360003, India
Abstract
In this paper, we introduce an exact solution for a Hayward black hole (BH) by incorporating anisotropic perfect fluid influenced by nonlinear electrodynamics and non commutative geometry. The solution obtained resembles de Sitter spacetime at a small value of $r$ ($r\to 0$) and at a large distance ($r\to \infty$) resembles the regular Schwarzschild geometry . In the absence of non commutative geometry the solution obtained interpolates with the Hayward BH and as non commutative geometry inspired BH in the absence of magnetic monopole charge. Non commutative geometry modifies thermodynamic properties of the BH. The calculation of Hawking temperature and its graphical analysis indicate that the temperature reaches its peak at the point of heat capacity divergence.
Keywords
Main Subjects
Article PDF
[1] S.W. Hawking, “Particle creation by black holes”, Commun. Math. Phys., 43(3), 199 (1975). DOI: 10.1007/BF02345020
[2] L. Susskind, “String theory and the principle of black hole complementarity”, Phys. Rev. Lett., 71(15), 2367 (1993). DOI: 10.1103/PhysRevLett.71.2367
[3] E. Witten, “Small instantons in string theory”, Nucl. Phys. B, 460(3), 541 (1996). DOI: 10.1016/0550-3213(95)00625-7
[4] N. Seiberg, and E. Witten, “String Theory and Noncommutative Geometry”, JHEP, 9909, 032 (1999). DOI: 10.1088/1126-6708/1999/09/032
[5] H.S. Snyder, “Quantized Space-Time”, Phys. Rev. 71, 38 (1947). DOI: 10.1103/PhysRev.71.38
[6] A. Smailagic, E. Spallucci, “Feynman path integral on the non-commutative plane”, J. Phys. A, 36, L467 (2003). DOI: 10.1088/0305-4470/36/33/101
[7] A. Smailagic, E. Spallucci, “UV divergence-free QFT on noncommutative plane”, J. Phys. A, 36, L517 (2003). DOI: 10.1088/0305-4470/36/39/103
[8] P. Nicolini, A. Smailagic, E. Spallucc, “Noncommutative Geometry Inspired Schwarzschild Black Hole”, Physics Letters B, 632, 547 (2006). DOI: 10.1016/j.physletb.2005.11.004
[9] P. Nicolini, A. Smailagic, E. Spallucc, “Non-commutative geometry inspired charged black holes”, Physics Letters B, 645, 261 (2007). DOI: 10.1016/j.physletb.2006.12.020
[10] D.V. Singh, S. Upadhyay, Y. Myrzakulov, K. Myrzakulov, B. Singh and M. Kumar, “Thermodynamic behavior and phase transitions of black holes with a cloud of strings and perfect fluid dark matter”, Nucl. Phys. B, 1016, 116915 (2025). DOI: 10.1016/j.nuclphysb.2025.116915
[11] A. Kumar, D. V. Singh and S. Upadhyay, “Impact of Perfect Fluid Dark Matter on the Thermodynamics of AdS Ayón-Beato-GarcÍa Black Holes”, JHAP, 4(4), 85 (2024). DOI: 10.22128/jhap.2024.884.1096
[12] A. Kumar, D. V. Singh and S. Upadhyay, “Ayón–Beato–García black hole coupled with a cloud of strings: Thermodynamics, shadows and quasinormal modes”, Int. J. Mod. Phys. A, 39(31), 2450136 (2024). DOI: 10.1142/S0217751X24501367
[13] H. K. Sudhanshu, D. V. Singh, S. Upadhyay, Y. Myrzakulov and K. Myrzakulov, “Thermodynamics of a newly constructed black hole coupled with nonlinear electrodynamics and cloud of strings”, Phys. Dark Univ., 46, 101648 (2024). DOI: 10.1016/j.dark.2024.101648
[14] B. Singh, D. Veer Singh and B. Kumar Singh, “Thermodynamics, phase structure and quasinormal modes for AdS Heyward massive black hole”, Phys. Scripta 99(2), 025305, (2024). DOI: 10.1088/1402-4896/ad1da4
[15] A. Kumar, D. V. Singh, Y. Myrzakulov, G. Yergaliyeva and S. Upadhyay, “Exact solution of Bardeen black hole in Einstein–Gauss–Bonnet gravity”, Eur. Phys. J. Plus, 138(12), 1071 (2023). DOI: 10.1140/epjp/s13360-023-04718-3
[16] B. Singh, B. K. Singh and D. V. Singh, “Thermodynamics, phase structure of Bardeen massive black hole in Gauss-Bonnet gravity”, Int. J. Geom. Meth. Mod. Phys., 20(8), 2350125 (2023). DOI: 10.1142/S0219887823501256
[17] S.H. Hendi, S. Panahiyan, B. Eslam Panah, and M. Momennia, “Phase transition of charged black holes in massive gravity through new methods”, Ann. Phys. (Berlin), 528(11-12), 819 (2016). DOI: 10.1002/andp.201600180
36 Indra Sen Ram et al.
[18] S.H. Hendi and M.H. Vahidinia, “Extended phase space thermodynamics and P-V criticality of black holes with a nonlinear source”, Phys. Rev. D, 88, 084045 (2013). DOI: 10.1103/PhysRevD.88.084045
[19] S.H. Hendi, , R.B. Mann, S. Panahiyan, and B. Eslam Panah, “Van der Waals like behavior of topological AdS black holes in massive gravity”, Phys. Rev. D, 95, 021501(R) (2017). DOI: 10.1103/PhysRevD.95.021501
[20] C. Gao, “Black holes with many horizons in the theories of nonlinear electrodynamics”, Phys. Rev. D, 104, 064038 (2021). DOI: 10.1103/PhysRevD.104.064038
[21] Y. Zhao and H. Cheng, “The thermodynamic stability and phase structure of the Einstein-Euler-Heisenberg-AdS black holes”, Chin. Phys. C, 48(12), 125106 (2024). DOI: 10.1088/1674-1137/ad79d4
[22] S. A. Hayward, “Formation and evaporation of regular black holes”, Phys. Rev. Lett., 96, 031103 (2006). DOI: 10.1103/PhysRevLett.96.031103
[23] D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Exact nonsingular black holes and thermodynamics”, Nucl. Phys. B, 981, 115854 (2022). DOI: 10.1016/j.nuclphysb.2022.115854
[24] A. Kumar, D. V. Singh and S. G. Ghosh, “Hayward black holes in Einstein–Gauss– Bonnet gravity”, Annals Phys., 419, 168214 (2020). DOI: 10.1016/j.aop.2020.168214
[25] D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Bardeen-like regular black holes in 5D Einstein-Gauss-Bonnet gravity”, Annals Phys., 412, 168025 (2020). DOI: 10.1016/j.aop.2019.168025
[26] A. Kumar, D. Veer Singh and S. G. Ghosh, “D-dimensional Bardeen-AdS black holes in Einstein-Gauss-Bonnet theory”, Eur. Phys. J. C, 79, 275 (2019). DOI: 10.1140/epjc/s10052-019-6773-9
[27] S. G. Ghosh, D. V. Singh and S. D. Maharaj, “Regular black holes in Einstein-GaussBonnet gravity”, Phys. Rev. D, 97, 104050 (2018). DOI: 10.1103/PhysRevD.97.104050
[28] S.H. Hendi, G.Q. Li, J.X. Mo, S. Panahiyan, and B. Eslam Panah, “New perspective for black hole thermodynamics in Gauss-Bonnet Born-Infeld massive gravity”, Eur. Phys. J. C, 76, 571 (2016). DOI: 10.1140/epjc/s10052-016-4410-4
[29] S.H. Hendi, B. Eslam Panah and S. Panahiyan, “Black Hole Solutions in Gauss- BonnetMassive Gravity in the Presence of Power- Maxwell Field”, Fortschr. Phys. (Prog. Phys.), 2018, 1800005 (2018). DOI: 10.1002/prop.201800005
[30] B. K. Vishvakarma, D. V. Singh and S. Siwach, “Parameter estimation of the BardeenKerr black hole in cloud of strings using shadow analysis”, Phys. Scripta, 99(2), 025022 (2024). DOI: 10.48550/arXiv.2310.20393
[31] B. Dolan, A. Kostouki, D. Kubizňák, and R. Mann, “Isolated critical point from Lovelock gravity”, Class. Quantum Grav., 31(24), 242001 (2014). DOI: 10.1088/0264- 9381/31/24/242001
[32] R. A. Hennigar, R. B. Mann, and E. Tjoa, “Superfluid Black Holes”, Phys. Rev. Lett., 118(2), 021301 (2017). DOI: 10.1103/PhysRevLett.118.021301
[33] S. W. Wei, Y. X. Liu, and R. B. Mann, “Repulsive Interactions and Universal Properties of Charged Anti–de Sitter Black Hole Microstructures” Phys. Rev. Lett., 123(7), 071103 (2019). DOI: 10.1103/PhysRevLett.123.071103
[34] X. X. Zeng, Y. W. Han, and D. Y. Chen, “Thermodynamics and weak cosmic censorship conjecture of BTZ black holes in extended phase space”, Chin. Phys. C, 43(10), 105104 (2019). DOI; 10.1088/1674-1137/43/10/105104
[35] K. J. He, G. P. Li, and X. Y. Hu, “Violations of the weak cosmic censorship conjecture in the higher dimensional f(R) black holes with pressure”, Eur. Phys. J. C, 80(3), 209 (2020). DOI: 10.1140/epjc/s10052-020-7669-4
[36] B. P. Dolan, “Pressure and volume in the first law of black hole thermodynamics” Class. Quantum Grav., 28, 235017 (2011). DOI: 10.1088/0264-9381/28/23/235017
[37] B. Hazarika and P. Phukon, “Topology of restricted phase space thermodynamics in Kerr-Sen-Ads black holes”, Nucl. Phys. B, 1012, 116837 (2025). DOI: 10.1016/j.nuclphysb.2025.116837
[38] A. Sood, M. S. Ali, J. K. Singh and S. G. Ghosh, “Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter*”, Chin. Phys. C, 48(6), 065109 (2024). DOI: 10.1088/1674-1137/ad361f
[39] F. Rahmani and M. Sadeghi, “The phase transition of 4D Yang–Mills charged GB AdS black hole with cloud of strings”, Mod. Phys. Lett. A, 39(35-36), 2450164 (2024). DOI: 10.1142/S0217732324501645
[40] Y. Sekhmani, J. Rayimbaev, G. G. Luciano, R. Myrzakulov and D. J. Gogoi, “Phase structure of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state”, Eur. Phys. J. C, 84(3), 227 (2024). DOI: 10.1140/epjc/s10052-024- 12597-w
[41] S. W. Wei and Y. X. Liu, “Thermodynamic nature of black holes in coexistence region”, Sci. China Phys. Mech. Astron., 67(5), 250412 (2024). DOI: 10.1007/s11433-023-2335-2
[42] X. Q. Li, H. P. Yan, L. L. Xing and S. W. Zhou, “Critical behavior of AdS black holes surrounded by dark fluid with Chaplygin-like equation of state”, Phys. Rev. D, 107(10), 104055 (2023). DOI: 10.1103/PhysRevD.107.104055
[43] G. G. Luciano and E. Saridakis, “P - v criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics”, JHEP, 12, 114 (2023). DOI: 10.1007/JHEP12(2023)114
[44] Z. M. Xu and R. B. Mann, “Thermodynamic supercriticality and complex phase diagram for the AdS black hole”, DOI: 10.48550/arXiv.2504.05708
[45] R. Somogyfoki and P. Ván, “Volume in the Extensive Thermodynamics of Black Holes”, [arXiv:2503.22482 [gr-qc]]
[46] A. Baruah and P. Phukon, “Restricted Phase Space Thermodynamics of 4D Dyonic AdS Black Holes: Insights from Kaniadakis Statistics and Emergence of Superfluid λ-Phase Transition”, [arXiv:2412.04375 [hep-th]]
[47] S. Masood and S. Mikki, “The thermodynamic profile of AdS black holes in Lorentz invariance-violating Bumblebee and Kalb-Ramond gravity”, [arXiv:2411.06188 [gr-qc]]
[48] Y. Z. Du, H. F. Li, Y. B. Ma and Q. Gu, “Topology and phase transition for EPYM AdS black hole in thermal potential”, Nucl. Phys. B, 1006, 116641 (2024). DOI: 10.1016/j.nuclphysb.2024.116641
[49] J. Yang and R. B. Mann, “Dynamic behaviours of black hole phase transitions near quadruple points”, JHEP, 08, 028 (2023). DOI: 10.1007/JHEP08(2023)028
[50] Z. F. Mai, R. Xu, D. Liang and L. Shao, “Extended thermodynamics of the bumblebee black holes”, Phys. Rev. D, 108(2), 024004 (2023). DOI: 10.1103/PhysRevD.108.024004
[51] K. S. Upadhyay, S. Upadhyay and B. P. Mandal, “Phantom BTZ black holes: Thermal properties under perturbative corrections”, Nucl. Phys. B, 1018, 117078 (2025). DOI:10.1016/j.nuclphysb.2025.117078
[52] V. K. Srivastava, S. Upadhyay, A. K. Verma, D. V. Singh, Y. Myrzakulov and K. Myrzakulov, “Exploring non-perturbative effects on quasi-topological black hole thermodynamics”, Phys. Dark Univ., 48, 101915 (2025). DOI: 10.1016/j.dark.2025.101915
[53] S. Soroushfar, H. Farahani and S. Upadhyay, “Non-perturbative correction to thermodynamics of conformally dressed 3D black hole”, Phys. Dark Univ., 42, 101272 (2023). DOI: 10.1016/j.dark.2023.101272
[54] S. Upadhyay and D. V. Singh, “Black hole solution and thermal properties in 4D AdS Gauss–Bonnet massive gravity”, Eur. Phys. J. Plus, 137(3), 383 (2022). DOI: 10.1140/epjp/s13360-022-02569-y
[55] B. Pourhassan and S. Upadhyay, “Perturbed thermodynamics of charged black hole solution in Rastall theory”, Eur. Phys. J. Plus, 136(3), 311 (2021). DOI: 10.1140/epjp/s13360-021-01271-9
[56] S. Upadhyay, “Leading-order corrections to charged rotating AdS black holes thermodynamics”, Gen. Rel. Grav., 50(10), 128 (2018). DOI: 10.1007/s10714-018-2459-0
[57] S. Upadhyay, “Quantum corrections to thermodynamics of quasitopological black holes”, Phys. Lett. B, 775, 130 (2017). DOI: 10.1016/j.physletb.2017.10.059
[58] M. Ma and R. Zhao, “Corrected form of the first law of thermodynamics for regular black holes”, Class. Quantun Grav., 31 245014 (2014). DOI: 10.1088/0264- 9381/31/24/245014
[59] R. V. Maluf and J. C. S. Neves, “Thermodynamics of a class of regular black holes with a generalized uncertainty principle”, Phys. Rev. D, 97, 104015 (2018). DOI: 10.1103/PhysRevD.97.104015
[60] B. K. Singh, R. P. Singh and D. V. Singh, “Extended phase space thermodynamics of Bardeen black hole in massive gravity”, Eur. Phys. J. Plus, 135(10), 862 (2020). DOI: 10.1140/epjp/s13360-020-00880-0
[61] D. V. Singh, M. S. Ali and S. G. Ghosh, “Noncommutative geometry inspired rotating black string”, Int. J. Mod. Phys. D, 27(12), 1850108 (2018). DOI: 10.1142/S0218271818501080
[62] F. Ahmed, D. V. Singh and S. G. Ghosh, “Five dimensional rotating regular black holes and shadow”, Gen. Rel. Grav., 54(2), 21 (2022). DOI: 10.1007/s10714-022-02906-7
[63] S. G. Ghosh, “A nonsingular rotating black hole”, Eur. Phys. J. C, 75(11), 532 (2015). DOI: 10.1140/epjc/s10052-015-3740-y
[64] D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Clouds of strings in 4D Einstein Gauss Bonnet black holes”, Phys. Dark Univ., 30, 100730 (2020). DOI: 10.1016/j.dark.2020.100730
[65] D. V. Singh and S. Siwach, “Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity”, Phys. Lett. B, 808, 135658 (2020). DOI: 10.1016/j.physletb.2020.135658
[66] S. G. Ghosh, D. V. Singh, R. Kumar and S. D. Maharaj, “Phase transition of AdS black holes in 4D EGB gravity coupled to nonlinear electrodynamics”, Annals Phys., 424, 168347 (2021). DOI: 10.1016/j.aop.2020.168347
[67] D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Bardeen-like regular black holes in 5D Einstein-Gauss-Bonnet gravity”, Annals Phys., 412, 168025 (2020). DOI: 10.1016/j.aop.2019.168025
[68] A. Kumar, D. Veer Singh and S. G. Ghosh, “D-dimensional Bardeen-AdS black holes in Einstein-Gauss-Bonnet theory”, Eur. Phys. J. C, 79(3), 275 (2019). DOI: 10.1140/epjc/s10052-019-6773-9
[69] D. V. Singh and S. Siwach, “Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity”, Phys. Lett. B, 808, 135658 (2020). DOI: 10.1016/j.physletb.2020.135658
[2] L. Susskind, “String theory and the principle of black hole complementarity”, Phys. Rev. Lett., 71(15), 2367 (1993). DOI: 10.1103/PhysRevLett.71.2367
[3] E. Witten, “Small instantons in string theory”, Nucl. Phys. B, 460(3), 541 (1996). DOI: 10.1016/0550-3213(95)00625-7
[4] N. Seiberg, and E. Witten, “String Theory and Noncommutative Geometry”, JHEP, 9909, 032 (1999). DOI: 10.1088/1126-6708/1999/09/032
[5] H.S. Snyder, “Quantized Space-Time”, Phys. Rev. 71, 38 (1947). DOI: 10.1103/PhysRev.71.38
[6] A. Smailagic, E. Spallucci, “Feynman path integral on the non-commutative plane”, J. Phys. A, 36, L467 (2003). DOI: 10.1088/0305-4470/36/33/101
[7] A. Smailagic, E. Spallucci, “UV divergence-free QFT on noncommutative plane”, J. Phys. A, 36, L517 (2003). DOI: 10.1088/0305-4470/36/39/103
[8] P. Nicolini, A. Smailagic, E. Spallucc, “Noncommutative Geometry Inspired Schwarzschild Black Hole”, Physics Letters B, 632, 547 (2006). DOI: 10.1016/j.physletb.2005.11.004
[9] P. Nicolini, A. Smailagic, E. Spallucc, “Non-commutative geometry inspired charged black holes”, Physics Letters B, 645, 261 (2007). DOI: 10.1016/j.physletb.2006.12.020
[10] D.V. Singh, S. Upadhyay, Y. Myrzakulov, K. Myrzakulov, B. Singh and M. Kumar, “Thermodynamic behavior and phase transitions of black holes with a cloud of strings and perfect fluid dark matter”, Nucl. Phys. B, 1016, 116915 (2025). DOI: 10.1016/j.nuclphysb.2025.116915
[11] A. Kumar, D. V. Singh and S. Upadhyay, “Impact of Perfect Fluid Dark Matter on the Thermodynamics of AdS Ayón-Beato-GarcÍa Black Holes”, JHAP, 4(4), 85 (2024). DOI: 10.22128/jhap.2024.884.1096
[12] A. Kumar, D. V. Singh and S. Upadhyay, “Ayón–Beato–García black hole coupled with a cloud of strings: Thermodynamics, shadows and quasinormal modes”, Int. J. Mod. Phys. A, 39(31), 2450136 (2024). DOI: 10.1142/S0217751X24501367
[13] H. K. Sudhanshu, D. V. Singh, S. Upadhyay, Y. Myrzakulov and K. Myrzakulov, “Thermodynamics of a newly constructed black hole coupled with nonlinear electrodynamics and cloud of strings”, Phys. Dark Univ., 46, 101648 (2024). DOI: 10.1016/j.dark.2024.101648
[14] B. Singh, D. Veer Singh and B. Kumar Singh, “Thermodynamics, phase structure and quasinormal modes for AdS Heyward massive black hole”, Phys. Scripta 99(2), 025305, (2024). DOI: 10.1088/1402-4896/ad1da4
[15] A. Kumar, D. V. Singh, Y. Myrzakulov, G. Yergaliyeva and S. Upadhyay, “Exact solution of Bardeen black hole in Einstein–Gauss–Bonnet gravity”, Eur. Phys. J. Plus, 138(12), 1071 (2023). DOI: 10.1140/epjp/s13360-023-04718-3
[16] B. Singh, B. K. Singh and D. V. Singh, “Thermodynamics, phase structure of Bardeen massive black hole in Gauss-Bonnet gravity”, Int. J. Geom. Meth. Mod. Phys., 20(8), 2350125 (2023). DOI: 10.1142/S0219887823501256
[17] S.H. Hendi, S. Panahiyan, B. Eslam Panah, and M. Momennia, “Phase transition of charged black holes in massive gravity through new methods”, Ann. Phys. (Berlin), 528(11-12), 819 (2016). DOI: 10.1002/andp.201600180
36 Indra Sen Ram et al.
[18] S.H. Hendi and M.H. Vahidinia, “Extended phase space thermodynamics and P-V criticality of black holes with a nonlinear source”, Phys. Rev. D, 88, 084045 (2013). DOI: 10.1103/PhysRevD.88.084045
[19] S.H. Hendi, , R.B. Mann, S. Panahiyan, and B. Eslam Panah, “Van der Waals like behavior of topological AdS black holes in massive gravity”, Phys. Rev. D, 95, 021501(R) (2017). DOI: 10.1103/PhysRevD.95.021501
[20] C. Gao, “Black holes with many horizons in the theories of nonlinear electrodynamics”, Phys. Rev. D, 104, 064038 (2021). DOI: 10.1103/PhysRevD.104.064038
[21] Y. Zhao and H. Cheng, “The thermodynamic stability and phase structure of the Einstein-Euler-Heisenberg-AdS black holes”, Chin. Phys. C, 48(12), 125106 (2024). DOI: 10.1088/1674-1137/ad79d4
[22] S. A. Hayward, “Formation and evaporation of regular black holes”, Phys. Rev. Lett., 96, 031103 (2006). DOI: 10.1103/PhysRevLett.96.031103
[23] D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Exact nonsingular black holes and thermodynamics”, Nucl. Phys. B, 981, 115854 (2022). DOI: 10.1016/j.nuclphysb.2022.115854
[24] A. Kumar, D. V. Singh and S. G. Ghosh, “Hayward black holes in Einstein–Gauss– Bonnet gravity”, Annals Phys., 419, 168214 (2020). DOI: 10.1016/j.aop.2020.168214
[25] D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Bardeen-like regular black holes in 5D Einstein-Gauss-Bonnet gravity”, Annals Phys., 412, 168025 (2020). DOI: 10.1016/j.aop.2019.168025
[26] A. Kumar, D. Veer Singh and S. G. Ghosh, “D-dimensional Bardeen-AdS black holes in Einstein-Gauss-Bonnet theory”, Eur. Phys. J. C, 79, 275 (2019). DOI: 10.1140/epjc/s10052-019-6773-9
[27] S. G. Ghosh, D. V. Singh and S. D. Maharaj, “Regular black holes in Einstein-GaussBonnet gravity”, Phys. Rev. D, 97, 104050 (2018). DOI: 10.1103/PhysRevD.97.104050
[28] S.H. Hendi, G.Q. Li, J.X. Mo, S. Panahiyan, and B. Eslam Panah, “New perspective for black hole thermodynamics in Gauss-Bonnet Born-Infeld massive gravity”, Eur. Phys. J. C, 76, 571 (2016). DOI: 10.1140/epjc/s10052-016-4410-4
[29] S.H. Hendi, B. Eslam Panah and S. Panahiyan, “Black Hole Solutions in Gauss- BonnetMassive Gravity in the Presence of Power- Maxwell Field”, Fortschr. Phys. (Prog. Phys.), 2018, 1800005 (2018). DOI: 10.1002/prop.201800005
[30] B. K. Vishvakarma, D. V. Singh and S. Siwach, “Parameter estimation of the BardeenKerr black hole in cloud of strings using shadow analysis”, Phys. Scripta, 99(2), 025022 (2024). DOI: 10.48550/arXiv.2310.20393
[31] B. Dolan, A. Kostouki, D. Kubizňák, and R. Mann, “Isolated critical point from Lovelock gravity”, Class. Quantum Grav., 31(24), 242001 (2014). DOI: 10.1088/0264- 9381/31/24/242001
[32] R. A. Hennigar, R. B. Mann, and E. Tjoa, “Superfluid Black Holes”, Phys. Rev. Lett., 118(2), 021301 (2017). DOI: 10.1103/PhysRevLett.118.021301
[33] S. W. Wei, Y. X. Liu, and R. B. Mann, “Repulsive Interactions and Universal Properties of Charged Anti–de Sitter Black Hole Microstructures” Phys. Rev. Lett., 123(7), 071103 (2019). DOI: 10.1103/PhysRevLett.123.071103
[34] X. X. Zeng, Y. W. Han, and D. Y. Chen, “Thermodynamics and weak cosmic censorship conjecture of BTZ black holes in extended phase space”, Chin. Phys. C, 43(10), 105104 (2019). DOI; 10.1088/1674-1137/43/10/105104
[35] K. J. He, G. P. Li, and X. Y. Hu, “Violations of the weak cosmic censorship conjecture in the higher dimensional f(R) black holes with pressure”, Eur. Phys. J. C, 80(3), 209 (2020). DOI: 10.1140/epjc/s10052-020-7669-4
[36] B. P. Dolan, “Pressure and volume in the first law of black hole thermodynamics” Class. Quantum Grav., 28, 235017 (2011). DOI: 10.1088/0264-9381/28/23/235017
[37] B. Hazarika and P. Phukon, “Topology of restricted phase space thermodynamics in Kerr-Sen-Ads black holes”, Nucl. Phys. B, 1012, 116837 (2025). DOI: 10.1016/j.nuclphysb.2025.116837
[38] A. Sood, M. S. Ali, J. K. Singh and S. G. Ghosh, “Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter*”, Chin. Phys. C, 48(6), 065109 (2024). DOI: 10.1088/1674-1137/ad361f
[39] F. Rahmani and M. Sadeghi, “The phase transition of 4D Yang–Mills charged GB AdS black hole with cloud of strings”, Mod. Phys. Lett. A, 39(35-36), 2450164 (2024). DOI: 10.1142/S0217732324501645
[40] Y. Sekhmani, J. Rayimbaev, G. G. Luciano, R. Myrzakulov and D. J. Gogoi, “Phase structure of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state”, Eur. Phys. J. C, 84(3), 227 (2024). DOI: 10.1140/epjc/s10052-024- 12597-w
[41] S. W. Wei and Y. X. Liu, “Thermodynamic nature of black holes in coexistence region”, Sci. China Phys. Mech. Astron., 67(5), 250412 (2024). DOI: 10.1007/s11433-023-2335-2
[42] X. Q. Li, H. P. Yan, L. L. Xing and S. W. Zhou, “Critical behavior of AdS black holes surrounded by dark fluid with Chaplygin-like equation of state”, Phys. Rev. D, 107(10), 104055 (2023). DOI: 10.1103/PhysRevD.107.104055
[43] G. G. Luciano and E. Saridakis, “P - v criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics”, JHEP, 12, 114 (2023). DOI: 10.1007/JHEP12(2023)114
[44] Z. M. Xu and R. B. Mann, “Thermodynamic supercriticality and complex phase diagram for the AdS black hole”, DOI: 10.48550/arXiv.2504.05708
[45] R. Somogyfoki and P. Ván, “Volume in the Extensive Thermodynamics of Black Holes”, [arXiv:2503.22482 [gr-qc]]
[46] A. Baruah and P. Phukon, “Restricted Phase Space Thermodynamics of 4D Dyonic AdS Black Holes: Insights from Kaniadakis Statistics and Emergence of Superfluid λ-Phase Transition”, [arXiv:2412.04375 [hep-th]]
[47] S. Masood and S. Mikki, “The thermodynamic profile of AdS black holes in Lorentz invariance-violating Bumblebee and Kalb-Ramond gravity”, [arXiv:2411.06188 [gr-qc]]
[48] Y. Z. Du, H. F. Li, Y. B. Ma and Q. Gu, “Topology and phase transition for EPYM AdS black hole in thermal potential”, Nucl. Phys. B, 1006, 116641 (2024). DOI: 10.1016/j.nuclphysb.2024.116641
[49] J. Yang and R. B. Mann, “Dynamic behaviours of black hole phase transitions near quadruple points”, JHEP, 08, 028 (2023). DOI: 10.1007/JHEP08(2023)028
[50] Z. F. Mai, R. Xu, D. Liang and L. Shao, “Extended thermodynamics of the bumblebee black holes”, Phys. Rev. D, 108(2), 024004 (2023). DOI: 10.1103/PhysRevD.108.024004
[51] K. S. Upadhyay, S. Upadhyay and B. P. Mandal, “Phantom BTZ black holes: Thermal properties under perturbative corrections”, Nucl. Phys. B, 1018, 117078 (2025). DOI:10.1016/j.nuclphysb.2025.117078
[52] V. K. Srivastava, S. Upadhyay, A. K. Verma, D. V. Singh, Y. Myrzakulov and K. Myrzakulov, “Exploring non-perturbative effects on quasi-topological black hole thermodynamics”, Phys. Dark Univ., 48, 101915 (2025). DOI: 10.1016/j.dark.2025.101915
[53] S. Soroushfar, H. Farahani and S. Upadhyay, “Non-perturbative correction to thermodynamics of conformally dressed 3D black hole”, Phys. Dark Univ., 42, 101272 (2023). DOI: 10.1016/j.dark.2023.101272
[54] S. Upadhyay and D. V. Singh, “Black hole solution and thermal properties in 4D AdS Gauss–Bonnet massive gravity”, Eur. Phys. J. Plus, 137(3), 383 (2022). DOI: 10.1140/epjp/s13360-022-02569-y
[55] B. Pourhassan and S. Upadhyay, “Perturbed thermodynamics of charged black hole solution in Rastall theory”, Eur. Phys. J. Plus, 136(3), 311 (2021). DOI: 10.1140/epjp/s13360-021-01271-9
[56] S. Upadhyay, “Leading-order corrections to charged rotating AdS black holes thermodynamics”, Gen. Rel. Grav., 50(10), 128 (2018). DOI: 10.1007/s10714-018-2459-0
[57] S. Upadhyay, “Quantum corrections to thermodynamics of quasitopological black holes”, Phys. Lett. B, 775, 130 (2017). DOI: 10.1016/j.physletb.2017.10.059
[58] M. Ma and R. Zhao, “Corrected form of the first law of thermodynamics for regular black holes”, Class. Quantun Grav., 31 245014 (2014). DOI: 10.1088/0264- 9381/31/24/245014
[59] R. V. Maluf and J. C. S. Neves, “Thermodynamics of a class of regular black holes with a generalized uncertainty principle”, Phys. Rev. D, 97, 104015 (2018). DOI: 10.1103/PhysRevD.97.104015
[60] B. K. Singh, R. P. Singh and D. V. Singh, “Extended phase space thermodynamics of Bardeen black hole in massive gravity”, Eur. Phys. J. Plus, 135(10), 862 (2020). DOI: 10.1140/epjp/s13360-020-00880-0
[61] D. V. Singh, M. S. Ali and S. G. Ghosh, “Noncommutative geometry inspired rotating black string”, Int. J. Mod. Phys. D, 27(12), 1850108 (2018). DOI: 10.1142/S0218271818501080
[62] F. Ahmed, D. V. Singh and S. G. Ghosh, “Five dimensional rotating regular black holes and shadow”, Gen. Rel. Grav., 54(2), 21 (2022). DOI: 10.1007/s10714-022-02906-7
[63] S. G. Ghosh, “A nonsingular rotating black hole”, Eur. Phys. J. C, 75(11), 532 (2015). DOI: 10.1140/epjc/s10052-015-3740-y
[64] D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Clouds of strings in 4D Einstein Gauss Bonnet black holes”, Phys. Dark Univ., 30, 100730 (2020). DOI: 10.1016/j.dark.2020.100730
[65] D. V. Singh and S. Siwach, “Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity”, Phys. Lett. B, 808, 135658 (2020). DOI: 10.1016/j.physletb.2020.135658
[66] S. G. Ghosh, D. V. Singh, R. Kumar and S. D. Maharaj, “Phase transition of AdS black holes in 4D EGB gravity coupled to nonlinear electrodynamics”, Annals Phys., 424, 168347 (2021). DOI: 10.1016/j.aop.2020.168347
[67] D. V. Singh, S. G. Ghosh and S. D. Maharaj, “Bardeen-like regular black holes in 5D Einstein-Gauss-Bonnet gravity”, Annals Phys., 412, 168025 (2020). DOI: 10.1016/j.aop.2019.168025
[68] A. Kumar, D. Veer Singh and S. G. Ghosh, “D-dimensional Bardeen-AdS black holes in Einstein-Gauss-Bonnet theory”, Eur. Phys. J. C, 79(3), 275 (2019). DOI: 10.1140/epjc/s10052-019-6773-9
[69] D. V. Singh and S. Siwach, “Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity”, Phys. Lett. B, 808, 135658 (2020). DOI: 10.1016/j.physletb.2020.135658
)
Volume 6, Issue 4
May 2026Pages 28-39
- Receive Date: 16 November 2025
- Revise Date: 15 December 2025
- Accept Date: 29 December 2025